We investigate the spin states obtained by extracting $n$ electrons from closed-shell fermionic states. A partition of the system is defined through the introduction of the extraction modes. We derive the expression of the $n$-body reduced density matrices, which represent the extracted spin states. We show that these states exhibit different forms of spin entanglement, whose detection is discussed in terms of the spin-squeezing inequalities.

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• Electronic structure of atoms & molecules
• Fermions
• Molecular magnetism
• Quantum correlations, foundations & formalism
• Molecules
• Qubits
• Magnetic moment
• Continuous symmetries in condensed matter
• Density matrix methods
• Electron-correlation calculations
• Spin lattice models